Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

Abstract

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel-Gasser-Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

Architecture-Dependent Anisotropic Hysteresis in Smooth Muscle Cells

“…Axial stresses were an order of magnitude higher than transverse stresses (Fig. 2, C and D), consistent with previous findings (23). Within the cycle, loading stresses were higher than the subsequent unloading (Fig.…”

“…The first Piola-Kirchhoff (PK1) stresses (force per unit undeformed cross-sectional area) at the cell's midline were calculated as P x ¼ ðf x =A x Þ and P y ¼ ðf y =A y Þ, where A x and A y are the cell midline cross-sectional areas ( Fig. S2 C), measured in a previous study to be A x ¼ 78 mm 2 and A y ¼ 278 mm 2 for VSMCs with an AR of 4, A x ¼ 94 mm 2 and A y ¼ 190 mm 2 for VSMCs with an AR of 2, and A x ¼ A y ¼ 117 mm 2 for VSMCs with an AR of 1 (23).…”

“…Micropatterned CmBS substrates were prepared as previously described (23). Briefly, VSMCs were micropatterned with aspect ratios (ARs) 4, 2, and 1 (AR4: 32 Â 128 mm; AR2: 91 Â 44 mm; AR1: 63 Â 63 mm) on polyacrylamide gels with Young's moduli of 13.5 kPa, which were adhered to elastomer membranes.…”

“…We used CmBS microscopy (23) to apply dynamic physiological deformations (up to 25% applied strain) to individual adherent VSMCs and concurrently measure the resulting stresses ( Fig. 1).…”

“…Time-dependent properties of cells have been characterized, but existing studies either measure small strain properties or do not account for structural anisotropy of the cell (19)(20)(21)(22). Recently, using cellular micro-biaxial stretching (CmBS) microscopy, we demonstrated that vascular smooth muscle cells (VSMCs) with native-like architecture have highly anisotropic mechanical properties under large strains due to their highly aligned actomyosin cytoskeleton (23). Here, we expand on that study to examine hysteresis in cyclically stretched VSMCs.…”